Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $R$ and $S$ be rings and $M$ be an $S$-$R$- bimodule. Then consider the triangular matrix ring constructed from these data (as, e.g., in Auslander-Reiten-Smalo). what one can say about the projective dimension of a (right) module $(X, Y)_f$ over this triangular matrix ring? Maybe I should explain that, in this situation, $X$ is a right $S$-module, $Y$ is a right $R$-module and $f: X\otimes_S M\longrightarrow Y$ is $R$-linear.

share|improve this question
    
As I said above, X is a right S-module, Y is a right R-module and f: X\otimes_S M\longrightarrow Y is R-linear. –  Nick Apr 10 at 15:25
    
Thanks for adding that info. –  rschwieb Apr 10 at 16:54

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.